You need to change the single apostrophe to double. Something like this:

Code:
Private Sub Command_Click()
    Dim SQLSearchString As String
    Dim strLastName As String
    
    strSQL = "select * from refuserinfo"
        
    rsTempRecordset.Open strSQL, cnRate, adOpenStatic, adLockReadOnly
    
    
    strLastName = "o'price"
    SQLSearchString = " lastname = '" & Replace(strLastName, "'", "''") & "'"
   
    If Not rsTempRecordset.EOF Then
        rsTempRecordset.Find SQLSearchString, , adSearchForward
        If rsTempRecordsetEOF Then
            MsgBox "No Records Found... Try Again"
        Else
            MsgBox "Records Found"
        End If
    End If
    
End Sub